Elliptic curve search results

Results (4 matches)

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
1296.1-a2	1296.1-a	$2$	$3$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1296.1	\( 2^{4} \cdot 3^{4} \)	\( 2^{16} \cdot 3^{12} \)	$2.45697$	$(-a+2), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3$	3B	$49$	\( 1 \)	$1$	$0.364059351$	3.892768911	\( 5646360960 a - 15760621008 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 765 a - 2151\) , \( 17544 a - 49002\bigr] \)	${y}^2={x}^{3}+\left(765a-2151\right){x}+17544a-49002$
1296.1-b2	1296.1-b	$2$	$3$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1296.1	\( 2^{4} \cdot 3^{4} \)	\( 2^{16} \cdot 3^{6} \)	$2.45697$	$(-a+2), (2)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3$	3B.1.1	$1$	\( 3^{2} \)	$1$	$4.812485434$	1.050170418	\( 5646360960 a - 15760621008 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -123 a - 231\) , \( -1536 a - 2738\bigr] \)	${y}^2={x}^{3}+\left(-123a-231\right){x}-1536a-2738$
1296.1-e2	1296.1-e	$2$	$3$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1296.1	\( 2^{4} \cdot 3^{4} \)	\( 2^{16} \cdot 3^{12} \)	$2.45697$	$(-a+2), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3$	3B	$1$	\( 1 \)	$1$	$7.068449444$	1.542462125	\( 5646360960 a - 15760621008 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -45 a - 234\) , \( 600 a + 1806\bigr] \)	${y}^2={x}^{3}+\left(-45a-234\right){x}+600a+1806$
1296.1-f2	1296.1-f	$2$	$3$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1296.1	\( 2^{4} \cdot 3^{4} \)	\( 2^{16} \cdot 3^{6} \)	$2.45697$	$(-a+2), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3$	3B.1.2	$1$	\( 3 \)	$1$	$1.604161811$	1.050170418	\( 5646360960 a - 15760621008 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 48 a - 159\) , \( 336 a - 874\bigr] \)	${y}^2={x}^{3}+\left(48a-159\right){x}+336a-874$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.